The long term objective of this project is to develop computational and statistical techniques for the study design and the analysis of complex familial diseases. This will aid in the identification of genes which contribute to disease susceptibility for complex diseases such as heart disease. The specific aims include development of methods for the computation and maximization of likelihoods of genetic models in order to fit models for complex genetic traits. These methods will provide the means of analyzing multilocus Mendelian models on extended complex pedigrees for polygenic models with genetic and environmental complexities and for mixed models, including linkage analysis with multiple marker loci. This project will also investigate the power of studies combining segregation and linkage analysis in the analysis of complex traits, and will investigate efficiencies of alternative sampling designs. The approach will employ simulation techniques based on the Gibbs sampler, a novel Monte Carlo technique now becoming widely used in Statistics. This technique provides samples from the distribution of genetic effects, conditional on observed phenotypic data, and thence facilitates efficient Monte Carlo estimation of likelihood ratios. Programs will be developed in order to perform several forms of data analysis, and to evaluate the performance of these techniques. Several datasets are available for use, including a large collection of pedigrees collected through the collaboration of one of the investigators in a study of the genetics and epidemiology of heart disease. Analyses include applications of Monte Carlo techniques to 1) determine multilocus haplotypes segregating in large complex genealogies, 2) fit polygenic models of quantitative measurements, such as Apolipoprotein B levels, associated with risk for heart disease, 3) fit multiple threshold models to data on rank-ordered categorical traits, and 4) perform segregation and linkage analysis of risk factors for heart disease. Methods will also be evaluated by the analysis of data simulated under models which include both polygenic and Mendelian effects which are associated with linked markers.